Quantum field simulator for dynamics in curved spacetime.

In most cosmological models, rapid expansion of space marks the first moments of the Universe and leads to the amplification of quantum fluctuations1. The description of subsequent dynamics and related questions in cosmology requires an understanding of the quantum fields of the standard model and dark matter in curved spacetime. Even the reduced problem of a scalar quantum field in an explicitly time-dependent spacetime metric is a theoretical challenge2-5, and thus a quantum field simulator can lead to insights. Here we demonstrate such a quantum field simulator in a two-dimensional Bose-Einstein condensate with a configurable trap6,7 and adjustable interaction strength to implement this model system. We explicitly show the realization of spacetimes with positive and negative spatial curvature by wave-packet propagation and observe particle-pair production in controlled power-law expansion of space, using Sakharov oscillations to extract amplitude and phase information of the produced state. We find quantitative agreement with analytical predictions for different curvatures in time and space. This benchmarks and thereby establishes a quantum field simulator of a new class. In the future, straightforward upgrades offer the possibility to enter unexplored regimes that give further insight into relativistic quantum field dynamics.

Observation of universal dynamics in a spinor Bose gas far from equilibrium.

Predicting the dynamics of quantum systems far from equilibrium represents one of the most challenging problems in theoretical many-body physics1,2. While the evolution of a many-body system is in general intractable in all its details, relevant observables can become insensitive to microscopic system parameters and initial conditions. This is the basis of the phenomenon of universality. Far from equilibrium, universality is identified through the scaling of the spatio-temporal evolution of the system, captured by universal exponents and functions. Theoretically, this has been studied in examples as different as the reheating process in inflationary Universe cosmology3,4, the dynamics of nuclear collision experiments described by quantum chromodynamics5,6, and the post-quench dynamics in dilute quantum gases in non-relativistic quantum field theory7-11. However, an experimental demonstration of such scaling evolution in space and time in a quantum many-body system has been lacking. Here we observe the emergence of universal dynamics by evaluating spatially resolved spin correlations in a quasi-one-dimensional spinor Bose-Einstein condensate12-16. For long evolution times we extract the scaling properties from the spatial correlations of the spin excitations. From this we find the dynamics to be governed by an emergent conserved quantity and the transport of spin excitations towards low momentum scales. Our results establish an important class of non-stationary systems whose dynamics is encoded in time-independent scaling exponents and functions, signalling the existence of non-thermal fixed points10,17,18. We confirm that the non-thermal scaling phenomenon involves no fine-tuning of parameters, by preparing different initial conditions and observing the same scaling behaviour. Our analogue quantum simulation approach provides the basis with which to reveal the underlying mechanisms and characteristics of non-thermal universality classes. One may use this universality to learn, from experiments with ultracold gases, about fundamental aspects of dynamics studied in cosmology and quantum chromodynamics.

Universal Dynamics of Rogue Waves in a Quenched Spinor Bose Condensate.

Isolated many-body systems far from equilibrium may exhibit scaling dynamics with universal exponents indicating the proximity of the time evolution to a nonthermal fixed point. We find universal dynamics connected with the occurrence of extreme wave excitations in the mutually coupled magnetic components of a spinor gas which propagate in an effectively random potential. The frequency of these rogue waves is affected by the time-varying spatial correlation length of the potential, giving rise to an additional exponent δ_{c}≃1/3 for temporal scaling, which is different from the exponent ß_{V}≃1/4 characterizing the scaling of the correlation length ℓ_{V}∼t^{ß_{V}} in time. As a result of the caustics, i.e., focusing events, real-time instanton defects appear in the Larmor phase of the spin-1 system as vortices in space and time. The temporal correlations governing the instanton occurrence frequency scale as t^{δ_{I}}. This suggests that the universality class of a nonthermal fixed point could be characterized by different, mutually related exponents defining the evolution in time and space, respectively. Our results have a strong relevance for understanding pattern coarsening from first principles and potential implications for dynamics ranging from the early Universe to geophysical dynamics and microphysics.

Detecting Entanglement Structure in Continuous Many-Body Quantum Systems.

A prerequisite for the comprehensive understanding of many-body quantum systems is a characterization in terms of their entanglement structure. The experimental detection of entanglement in spatially extended many-body systems describable by quantum fields still presents a major challenge. We develop a general scheme for certifying entanglement and demonstrate it by revealing entanglement between distinct subsystems of a spinor Bose-Einstein condensate. Our scheme builds on the spatially resolved simultaneous detection of the quantum field in two conjugate observables which allows the experimental confirmation of quantum correlations between local as well as nonlocal partitions of the system. The detection of squeezing in Bogoliubov modes in a multimode setting illustrates its potential to boost the capabilities of quantum simulations to study entanglement in spatially extended many-body systems.

Dating glacier ice of the last millennium by quantum technology.

Radiometric dating with 39Ar covers a unique time span and offers key advances in interpreting environmental archives of the last millennium. Although this tracer has been acknowledged for decades, studies so far have been limited by the low abundance and radioactivity, thus requiring huge sample sizes. Atom trap trace analysis, an application of techniques from quantum physics such as laser cooling and trapping, allows us to reduce the sample volume by several orders of magnitude compared with conventional techniques. Here we show that the adaptation of this method to 39Ar is now available for glaciological applications, by demonstrating the entire process chain for dating of alpine glacier ice by argon trap trace analysis (ArTTA). Ice blocks as small as a few kilograms are sufficient and have been obtained at two artificial glacier caves. Importantly, both sites offer direct access to the stratigraphy at the glacier base and validation against existing age constraints. The ice blocks obtained at Chli Titlis glacier at 3,030 m asl (Swiss Alps) have been dated by state-of-the-art microradiocarbon analysis in a previous study. The unique finding of a bark fragment and a larch needle within the ice of Schaufelferner glacier at 2,870 m asl (Stubai Alps, Austria) allows for conventional radiocarbon dating. At both sites the existing age information based on radiocarbon dating and visual stratigraphy corroborates the 39Ar ages. With our results, we establish argon trap trace analysis as the key to decipher so far untapped glacier archives of the last millennium.

Collisions of Three-Component Vector Solitons in Bose-Einstein Condensates.

Ultracold gases provide an unprecedented level of control for the investigation of soliton dynamics and collisions. We present a scheme for deterministically preparing pairs of three-component solitons in a Bose-Einstein condensate. Our method is based on local spin rotations which simultaneously imprint suitable phase and density distributions. This enables us to observe striking collisional properties of the vector degree of freedom which naturally arises for the coherent nature of the emerging multicomponent solitons. We find that the solitonic properties in the quasi-one-dimensional system are quantitatively described by the integrable repulsive three-component Manakov model.

Simultaneous Readout of Noncommuting Collective Spin Observables beyond the Standard Quantum Limit.

We augment the information extractable from a single absorption image of a spinor Bose-Einstein condensate by coupling to initially empty auxiliary hyperfine states. Performing unitary transformations in both the original and auxiliary hyperfine manifold enables the simultaneous measurement of multiple spin-1 observables. We apply this scheme to an elongated atomic cloud of ^{87}Rb to simultaneously read out three orthogonal spin directions and with that directly access the spatial spin structure. The readout even allows the extraction of quantum correlations which we demonstrate by detecting spin-nematic squeezing without state tomography.

Dissipative Double-Well Potential for Cold Atoms: Kramers Rate and Stochastic Resonance.

We experimentally study particle exchange in a dissipative double-well potential using laser-cooled atoms in a hybrid trap. We measure the particle hopping rate as a function of barrier height, temperature, and atom number. Single-particle resolution allows us to measure rates over more than 4 orders of magnitude and distinguish the effects of loss and hopping. Deviations from the Arrhenius-law scaling at high barrier heights occur due to cold collisions between atoms within a well. By driving the system periodically, we characterize the phenomenon of stochastic resonance in the system response.

High signal to noise absorption imaging of alkali atoms at moderate magnetic fields.

We present an improved scheme for absorption imaging of alkali atoms at moderate magnetic fields, where the excited state is well in the Paschen-Back regime, but the ground state hyperfine manifold is not. It utilizes four atomic levels to obtain an approximately closed optical cycle. With the resulting absorption of the corresponding two laser frequencies, we extract the atomic column density of a 39K Bose-Einstein condensate. The scheme can be readily applied to all other alkali-like species.

Classical bifurcation at the transition from Rabi to Josephson dynamics.

We report on the experimental demonstration of the internal bosonic Josephson effect in a rubidium spinor Bose-Einstein condensate. The measurement of the full time dynamics in phase space allows the characterization of the theoretically predicted π-phase modes and quantitatively confirms analytical predictions, revealing a classical bifurcation. Our results suggest that this system is a model system which can be tuned from classical to the quantum regime and thus is an important step towards the experimental investigation of entanglement generation close to critical points.

A scalable realization of local U(1) gauge invariance in cold atomic mixtures.

In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is the quantum theory of electrons interacting with the electromagnetic field, based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. Although quantum computers suggest a way forward, large-scale digital quantum devices for complex simulations are difficult to build. We propose a scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. Using interspecies spin-changing collisions in an atomic mixture, we achieve gauge-invariant interactions between matter and gauge fields with spin- and species-independent trapping potentials. We experimentally realize the elementary building block as a key step toward a platform for quantum simulations of continuous gauge theories.

39Ar dating with small samples provides new key constraints on ocean ventilation.

Ocean ventilation is the integrated effect of various processes that exchange surface properties with the ocean interior and is essential for oxygen supply, storage of anthropogenic carbon and the heat budget of the ocean, for instance. Current observational methods utilise transient tracers, e.g. tritium, SF6, CFCs and 14C. However, their dating ranges are not ideal to resolve the centennial-dynamics of the deep ocean, a gap filled by the noble gas isotope 39Ar with a half-life of 269 years. Its broad application has been hindered by its very low abundance, requiring 1000 L of water for dating. Here we show successful 39Ar dating with 5 L of water based on the atom-optical technique Atom Trap Trace Analysis. Our data reveal previously not quantifiable ventilation patterns in the Tropical Atlantic, where we find that advection is more important for the ventilation of the intermediate depth range than previously assumed. Now, the demonstrated analytical capabilities allow for a global collection of 39Ar data, which will have significant impact on our ability to quantify ocean ventilation.

Spatially distributed multipartite entanglement enables EPR steering of atomic clouds.

A key resource for distributed quantum-enhanced protocols is entanglement between spatially separated modes. However, the robust generation and detection of entanglement between spatially separated regions of an ultracold atomic system remain a challenge. We used spin mixing in a tightly confined Bose-Einstein condensate to generate an entangled state of indistinguishable particles in a single spatial mode. We show experimentally that this entanglement can be spatially distributed by self-similar expansion of the atomic cloud. We used spatially resolved spin read-out to reveal a particularly strong form of quantum correlations known as Einstein-Podolsky-Rosen (EPR) steering between distinct parts of the expanded cloud. Based on the strength of EPR steering, we constructed a witness, which confirmed genuine 5-partite entanglement.

Universal equilibrium scaling functions at short times after a quench.

By analyzing spin-spin correlation functions at relatively short distances, we show that equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.

Quantum metrology. Fisher information and entanglement of non-Gaussian spin states.

Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian statistics. Here, we report on the creation and characterization of non-Gaussian many-body entangled states. We develop a general method to extract the Fisher information, which reveals that the quantum dynamics of a classically unstable system creates quantum states that are not spin squeezed but nevertheless entangled. The extracted Fisher information quantifies metrologically useful entanglement, which we confirm by Bayesian phase estimation with sub-shot-noise sensitivity. These methods are scalable to large particle numbers and applicable directly to other quantum systems.

Noise thermometry with two weakly coupled Bose-Einstein condensates.

Here we report on the experimental investigation of thermally induced fluctuations of the relative phase between two Bose-Einstein condensates which are coupled via tunneling. The experimental control over the coupling strength and the temperature of the thermal background allows for the quantitative analysis of the phase fluctuations. Furthermore, we demonstrate the application of these measurements for thermometry in a regime where standard methods fail. With this we confirm that the heat capacity of an ideal Bose gas deviates from that of a classical gas as predicted by the third law of thermodynamics.

Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction.

We report on the first realization of a single bosonic Josephson junction, implemented by two weakly linked Bose-Einstein condensates in a double-well potential. In order to fully investigate the nonlinear tunneling dynamics we measure the density distribution in situ and deduce the evolution of the relative phase between the two condensates from interference fringes. Our results verify the predicted nonlinear generalization of tunneling oscillations in superconducting and superfluid Josephson junctions. Additionally, we confirm a novel nonlinear effect known as macroscopic quantum self-trapping, which leads to the inhibition of large amplitude tunneling oscillations.

Quantum features in atomic nanofabrication using exactly resonant standing waves.

We report on the first fabrication of nanostructures with exactly resonant light revealing the quantum character of the atom-light interaction. Classically the formation of nanostructures is not expected; thus, the observed formation of complex periodic line patterns can be explained only by treating atom-light interaction and propagation of the atoms quantum mechanically. Our numerical quantum calculations are in quantitative agreement with this experimental finding. Moreover, the theory predicts that for small detunings nanostructures with lambda/4 period can be produced, which beats the standard nanofabrication limit of lambda/2. Our experiments confirm this prediction.